A Caginalp phase-field system with a nonlinear coupling

DOI10.1016/j.nonrwa.2009.10.008zbMath1197.35082OpenAlexW2161089738MaRDI QIDQ984573

Alain Miranville, Ramón Quintanilla

Publication date: 20 July 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2009.10.008

zbMATH Keywords

dissipativitywell-posednesstype III thermoelasticitysemi-infinite cylinderspatial behavior of the solutions

Mathematics Subject Classification ID

Thermal effects in solid mechanics (74F05) Initial-boundary value problems for systems of nonlinear higher-order PDEs (35G61)

Related Items

Global and exponential attractors for a Caginalp type phase-field problem, Numerical analysis of a Caginalp phase-field system in type III heat conduction, Optimal control of a nonconserved phase field model of Caginalp type with thermal memory and double obstacle potential, A phase-field model based on a three-phase-lag heat conduction, A type III phase-field system with a logarithmic potential, Sliding mode control for a generalization of the Caginalp phase-field system, On the Caginalp phase-field system based on the Cattaneo law with nonlinear coupling, Phase-field system with two temperatures and a nonlinear coupling term, ON THE CAGINALP PHASE-FIELD SYSTEM BASED ON TYPE Ⅲ WITH TWO TEMPERATURES AND NONLINEAR COUPLING, Study of the dissipativity, global attractor and exponential attractor for a hyperbolic relaxation of the Caginalp phase-field system with singular nonlinear terms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Robust exponential attractors for a phase-field system with memory
• The non-isothermal Allen-Cahn equation with dynamic boundary conditions
• On the Caginalp system with dynamic boundary conditions and singular potentials.
• A generalization of the Caginalp phase-field system based on the Cattaneo law
• An analysis of a phase field model of a free boundary
• Thermoelasticity without energy dissipation
• Infinite-dimensional dynamical systems in mechanics and physics.
• A phase field system with memory: Global existence
• Existence of a universal attractor for a fully hyperbolic phase-field system
• Hysteresis and phase transitions
• Convergence to equilibrium for a parabolic-hyperbolic phase field model with Cattaneo heat flux law
• Long time behavior of solutions to the Caginalp system with singular potential
• Asymptotic behavior of solutions to the phase-field equations with Neumann boundary condi\-tions
• Stability in thermoelasticity of type III
• Growth and uniqueness in thermoelasticity
• Long-time convergence of solutions to a phase-field system
• A note on discontinuity waves in type III thermoelasticity
• A re-examination of the basic postulates of thermomechanics
• Some generalizations of the Caginalp phase-field system
• Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions
• Decay estimates for the constrained elastic cylinder of variable cross section
• On the impossibility of localization in linear thermoelasticity
• Asymptotic behavior of a nonisothermal Ginzburg-Landau model
• Convergence to equilibrium for a fully hyperbolic phase‐field model with Cattaneo heat flux law
• Finite dimensional exponential attractor for the phase field model
• Long-time behaviour for a model of phase-field type
• Uniform attractors for a phase-field model with memory and quadratic nonlinearity
• Energy bounds for some non-standard problems in thermoelasticity
• Well‐posedness and long time behavior of a parabolic‐hyperbolic phase‐field system with singular potentials
• Long-time stabilization of solutions to a phase-field model with memory
• Damping of end effects in a thermoelastic theory
• Hyperbolic phase-field dynamics with memory